My son shattered his hand/wrist back in 2001, he had to wait for swelling to go down before the surgeon could repair it..
It did take awhile and he lucked out with a top rated ortho surgeon doing the fix..

The clawing is usually a nerve issue, it could be trapped or pinched anywhere up into the neck & shoulder too, is PT working higher up the arm & shoulder as well as the hand?
When you fell the whole arm /shoulder probably took a jarring hit.

If you can find a place that has low level laser (LLLT - also called soft /cold laser), might be worth a try for healing & pain relief.. If PT places don't have it look at chiros.. just say you mainly want LLLT , unless you want to try adjustments too..